{"title":"Analysis and Numerical Simulation of the Initial–Boundary Value Problem for Quasilinear Equations of Complex Heat Transfer","authors":"A. Yu. Chebotarev, N. M. Pak, A. E. Kovtanyuk","doi":"10.1134/S1990478923040026","DOIUrl":null,"url":null,"abstract":"<p> We consider an initial–boundary value problem for quasilinear equations of complex heat\ntransfer that model the process of endovenous laser ablation. A priori estimates for the solution\nare obtained. Results on the global unique solvability of the problem are presented. An algorithm\nfor finding a solution of the initial–boundary value problem is proposed. The efficiency of the\nalgorithm is illustrated by numerical examples. The influence of internal thermal radiation on the\nbehavior of temperature fields is evaluated.\n</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"17 4","pages":"698 - 709"},"PeriodicalIF":0.5800,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied and Industrial Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1134/S1990478923040026","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}
引用次数: 0
Abstract
We consider an initial–boundary value problem for quasilinear equations of complex heat
transfer that model the process of endovenous laser ablation. A priori estimates for the solution
are obtained. Results on the global unique solvability of the problem are presented. An algorithm
for finding a solution of the initial–boundary value problem is proposed. The efficiency of the
algorithm is illustrated by numerical examples. The influence of internal thermal radiation on the
behavior of temperature fields is evaluated.
期刊介绍：
Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.
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